I've been following the thread for a while and have recently started doing questions from the STEP 2 papers.

I don't want to peek into the official solutions and I don't have someone to ask so would anyone be willing to have a look through some of my solutions to questions in the 2000 paper and give me some feedback?

I've been following the thread for a while and have recently started doing questions from the STEP 2 papers.

I don't want to peek into the official solutions and I don't have someone to ask so would anyone be willing to have a look through some of my solutions to questions in the 2000 paper and give me some feedback?

(Original post by Maths.)
Here is my solution to the second question of the paper, sorry this took a while as all my previous attempts to upload failed...

Seeing as they're all busy and I'm the complete opposite right now I'll have a look.

I think your solution is fine and you'd probably get full marks. A very minor point first: instead of saying 'where g(x)/h(x) is a function of x' it'd probably better to say 'where g(x)/h(x) is a polynomial.'

Probably the most important improvement to your solution would be your demonstration of p'''(a)=0. The easiest way is to simplify at each stage. So when you get your expression for p'(x), you can say 'therefore we can write p(x)=(x-a)^3 q(x) for some polynomial q(x),' then differentiate that to get p''(x) and deduce that you can write p''(x)=(x-a)^2 r(x) for some polynomial r(x) etc. This saves a lot of writing/calculation and therefore would save you time and reduce chances of making mistakes and dropping silly marks. In STEP it's essential to keep everything as simple as possible (without compromising necessary details of course).

Another minor point: probably just say that (x-a)^4 a factor of p(x) implies that p'''(a)=0 so that you directly get an equation for a and then you can go on to test the values as you did. It's just a bit clearer to do it like this, directly using what was proven in the first part.

(Original post by IrrationalRoot)
Seeing as they're all busy and I'm the complete opposite right now I'll have a look.

I think your solution is fine and you'd probably get full marks. A very minor point first: instead of saying 'where g(x)/h(x) is a function of x' it'd probably better to say 'where g(x)/h(x) is a polynomial.'

Probably the most important improvement to your solution would be your demonstration of p'''(a)=0. The easiest way is to simplify at each stage. So when you get your expression for p'(x), you can say 'therefore we can write p(x)=(x-a)^3 q(x) for some polynomial q(x),' then differentiate that to get p''(x) and deduce that you can write p''(x)=(x-a)^2 r(x) for some polynomial r(x) etc. This saves a lot of writing/calculation and therefore would save you time and reduce chances of making mistakes and dropping silly marks. In STEP it's essential to keep everything as simple as possible (without compromising necessary details of course).

Another minor point: probably just say that (x-a)^4 a factor of p(x) implies that p'''(a)=0 so that you directly get an equation for a and then you can go on to test the values as you did. It's just a bit clearer to do it like this, directly using what was proven in the first part.

Good morning IrrationalRoot and thank you so much for taking the time to give me a concise feedback, I'm sure it'll help great deal. I've printed a copy to check it out on my way to school.
Thanks again

(Original post by Maths.)
Good morning IrrationalRoot and thank you so much for taking the time to give me a concise feedback, I'm sure it'll help great deal. I've printed a copy to check it out on my way to school.
Thanks again

Hey guys, I've been preparing by myself for quite a while now, and it has been effective. I've been
invited to a very small STEP preparation group in my local area as one of my teachers got in
contact with people who have successfully prepared students to meet their Camb
offers.A lot of their students exceeded their offers. And some went to Ivy-Leagues instead. As I think my prep has gone well, I'm mulling over this.

If anyone from a state-school knows what I'm on about, how was your experience? Is it worth it?

(Original post by Injective)
Hey guys, I've been preparing by myself for quite a while now, and it has been effective. I've been
invited to a very small STEP preparation group in my local area as one of my teachers got in
contact with people who have successfully prepared students to meet their Camb
offers.A lot of their students exceeded their offers. And some went to Ivy-Leagues instead. As I think my prep has gone well, I'm mulling over this.

If anyone from a state-school knows what I'm on about, how was your experience? Is it worth it?

I was with Luciano for MAT yesterday(will be there on Friday, too) lol, but no not for STEP. My maths teacher has contacts with a private company in central, who do pro-bono stuff for state-educated students.

(Original post by Injective)
I was with Luciano for MAT yesterday(will be there on Friday, too) lol, but no not for STEP. My maths teacher has contacts with a private company in central, who do pro-bono stuff for state-educated students.

You can go if you like, but in my experience, there's nothing that's going to help with STEP other than sitting down on your own and working through questions.